Đáp án:
$\begin{array}{l}
a)\Delta > 0\\
\Rightarrow {m^2} - 4\left( {m - 1} \right) > 0\\
\Rightarrow {m^2} - 4m + 4 > 0\\
\Rightarrow {\left( {m - 2} \right)^2} > 0\\
\Rightarrow m \ne 2\\
b)m \ne 2\\
Theo\,Viet:\left\{ \begin{array}{l}
{x_1} + {x_2} = m\\
{x_1}{x_2} = m - 1
\end{array} \right.\\
x_1^3 + x_2^3 = 26\\
\Rightarrow {\left( {{x_1} + {x_2}} \right)^3} - 3{x_1}{x_2}\left( {{x_1} + {x_2}} \right) = 26\\
\Rightarrow {m^3} - 3\left( {m - 1} \right).m = 26\\
\Rightarrow {m^3} - 3{m^2} + 3m - 26 = 0\\
\Rightarrow m = 3,92\left( {tmdk} \right)
\end{array}$